The potential roots of the function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex] are -10,-5,3,15.
Given function p(x)=[tex]x^{3}+6x^{2} -7x-60[/tex]
We have to find the potential roots of the function according to rational root theorem.
Root is the solution of an equation usually expressed as a number or an algebraic formula.
The rational root theorem is used to find the potential roots of function.
For a polynomial function:
p(x)=p[tex]x^{n}[/tex]+..............................+q
The potential roots are:
Roots =±factors of q/factors of p
Th factors of 60 are =±1,±2,±3,±4,±5,±6,±10,±12.
The factors of 1 is ±1.
So we have factors are:±1,±2,±3,±4,±5,±6,±10,±12,±15,±20/±1
The roots are =±1,±2,±3,±4,±5,±6,±0.
Factors:-10,-5,3,15.
Hence the potential roots are -10,-5,3,15.
Question is incomplete as it should includes options :-10,-7,-5,3,15,24
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Jason planted and staked a tree. The stakes are 21 ft from the base of the tree. They are connected to wires that attach to the trunk at a height of 20 ft. Find the length of a wire. O14 ft 15 ft 20 ft 29 ft Jason planted and staked a tree . The stakes are 21 ft from the base of the tree . They are connected to wires that attach to the trunk at a height of 20 ft . Find the length of a wire . O14 ft 15 ft 20 ft 29 ft
Answer:
29 ft
Step-by-step explanation:
The distance along the ground from one stake to the tree, 21 ft, and the distance up the trunk from the ground, 20 ft, are the legs of a right triangle. The length of the wire is the hypotenuse of the right triangle. We can use the Pythagorean theorem to solve this problem.
a² + b² = c²
(21 ft)² + (20 ft)² = c²
c² = 841 ft²
c = √(841 ft²)
c = 29 ft
Answer: 29 ft
What is the value of the following radical expression?
Answer:
b.) 2
Explanation:
Given:
[tex]\sf - \sqrt[\sf 5]{\sf -32}[/tex]rewrite knowing 2⁵ = 32, (-2)⁵ = -32
[tex]\sf -\left(\sqrt[5]{(-2)^5}\right)[/tex]simplify, ⁿ√xⁿ = x
[tex]\sf -\left(-2}\right)[/tex]distribute inside parenthesis
[tex]\sf 2[/tex][tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{-a}=-\sqrt[n]{a}, if \ n \ is \ odd \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{-32}=-\sqrt[5]{32} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{32}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Decompose \ the \ number \ into \ prime \ factors: 32=2^{5}. \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=-\left(-\sqrt[5]{2^5}\right)} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^n}=a,\:\quad \:a\ge 0 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt[5]{2^5}=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf Remove \ parentheses:\quad \:-\left(-2\right)=2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{=2 \ \ \to \ \ \ Answer} \end{gathered}$}[/tex]
{ Pisces04 }What is the domain of the following relation?
{(-3, -8), (-2, 9), (1, -1), (5,3)}
O {-8, -1, 3, 9}
O {-3, -2, 1, 5}
O (-3, -8)
O {-8, -3, -2, -1, 1, 3, 5, 9}
Answer: {-3, -2, 1, 5}
Step-by-step explanation:
The domain is the set of x-values.
n August 31 of the current year, the assets and liabilities of Gladstone, Inc. are as follows: Cash $27,900; Supplies, $900; Equipment, $8,500; Accounts Payable, $7,300. What is the amount of stockholders’ equity as of August 31 of the current year?
The amount of stockholders’ equity as of August 31 of the current year is $26400.
How to calculate the equity?The owner's equity will be:
= Cash + Supplies + Equipment - Account payable
= 27900 + 900 + 8500 - 7300
= 26400
Therefore, the amount of stockholders’ equity as of August 31 of the current year is
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Kristina invests a total of $28,500 in two accounts. The first account earned a rate of return of 10% (after a year). However, the second account suffered a 4% loss in the same time period. At the end of one year, the total amount of money gained was $1,310.00. How much was invested into each account?
$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of money invested at 10% and y represent the amount of money invested at a loss of 4%, hence:
x + y = 28500 (1)
Also:
(x * 1 year * 0.1) + (y * 1 year * -0.04) = 1310
0.1x - 0.04y = 1310 (2)
From equation 1 and 2:
x = 17500, y = 11000
$17500 was invested in the first account at a rate of return of 10% (after a year) while $11000 was invested in the second account at a rate of 4% loss over the same period.
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Which is the equation in slope-intercept form for the line that passes through (−1, 5) and is parallel to 3x + 2y = 4?
y=−23x+72
y=−32x+72
y=32x−72
y=23x+72
Answer:
[tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
Step-by-step explanation:
So when two lines are parallel there slopes are the same, but there y-intercepts are different, since if they had the same y-intercept, then they would be the same exact line. To convert an equation into slope-intercept form you simple isolate y by moving everything else to the other side, and then divide by the coefficient of y so the coefficient of y becomes 1. This will give you the equation in the form: y=mx+b where m is the slope and b is the y-intercept (because when the linear equation crosses the y-axis, the x is 0, thus mx will be 0, leaving only b, so the y-intercept is b).
Original Equation:
3x + 2y = 4
Subtract 3x from both sides
2y = -3x + 4
Divide both sides by 2
y = -3/2x + 2
Generally any parallel line will be in the form:
[tex]y=-\frac{3}{2}x + b\ \ \ \ \ b\ne2[/tex]. Since as stated before if two lines have the same slope and y-intercept, they're the same line, which is not the same as parallel, since parallel lines never intersect.
So since we're given a point in the parallel line (-1, 5) we can plug those values into the equation to find the value of b
[tex]5=-\frac{3}{2}(-1) + b[/tex]
Multiply and
[tex]5=\frac{3}{2}+ b[/tex]
Convert 5 into a fraction with a denominator of 2
[tex]\frac{5}{1} * \frac{2}{2} = \frac{10}{2}[/tex]
Write equation using this form of 5:
[tex]\frac{10}{2}=\frac{3}{2}+b[/tex]
Subtract 3/2 from both sides
[tex]\frac{7}{2}=b[/tex]
Now take this value and input it into the slope-intercept form to finish the equation: [tex]y=-\frac{3}{2}x+\frac{7}{2}[/tex]
a survey of 504 citizens found that 378 of them favor a new bill introduced by the city. We want to find a 95% confidence interval for the true proportion of the population who favor the bill. What is the lower limit of the interval? (Round to 3 decimal digits)
The lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
What is a confidence interval?It is defined as the sampling distribution following an approximately normal distribution for known standard deviation.
We have:
A survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
Sample proportion = p = 378/504 = 0.75
q = 1 - p = 1 - 0.75 = 0.25
[tex]\rm SD = \sqrt{\dfrac{pq}{n}}[/tex]
[tex]\rm SD = \sqrt{\dfrac{0.75\times0.25}{504}}[/tex]
SD = 0.01928
For 95% confidence interval Z value = 1.96
Lower limit = 0.75 - 1.96(0.01928)
= 0.712
Thus, the lower limit of the interval is 0.712 if the survey of 504 citizens found that 378 of them favor a new bill introduced by the city.
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z varies directly as x^3 and inversely as y^3. if z=59 when x=8 and y=8, find Z if x=3 and y=4
[tex]z=\dfrac{kx^3}{y^3}\\\\\\59=\dfrac{k\cdot 8^3}{8^3}\\k=59\\\\\\z=\dfrac{59x^3}{y^3}\\\\\\z=\dfrac{59\cdot 3^3}{4^3}=\dfrac{1593}{64}[/tex]
A shirt and a tie together cost $57. The shirt costs $33 more than the tie. What is the cost of the shirt?
Answer:
Shirt: $45 , Tie: $12
Step-by-step explanation:
Let s be the price of the shirt
Let t be the price of the tie
Given the information from the question,
s + t = 57 - Equation 1
s - t = 33 - Equation 2
We will use substitution method to find the prices.
We will rearranging equation 1.
s = 57 - t
We will substitute s into equation 2.
57 - t - t = 33
57 - 2t = 33
-2t = 33 - 57
-2t = -24
t = -24 / -2
= 12
We now substitute t into Equation 1.
s + 12 = 57
s = 57 - 12
= 45
From here we know, the shirt costs $45 and the tie costs $12
Does anyone how to solve this sum? It’s urgent
The required value for the sum is 9580.
[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]
Simplification in mathematics to solve the given condition on its operators.
[tex]\frac{10000}{(1+\frac{0.115}{4})^2}+68\frac{1-\frac{1}{(1+\frac{0.115}{4})^2}}{\frac{0.115}{4}}[/tex]
= [tex]\frac{10000}{1.028^2} +68*\frac{1-\frac{1}{1.028^2} }{\frac{0.115}{4} } \\9451+68*\frac{1-0.94}{\frac{0.115}{4} } \\\\9451+68*\frac{0.054}{\frac{0.115}{4} } \\\\\\9451+3.72{\frac{4}{0.115} } \\\\\\9451+129\\[/tex]
= 9580
The required solution is given as 9580.
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please help me im d-mb
Answer:
5621 years
Step-by-step explanation:
Plug everything in first.
[tex]N=N_0e^{-kt}\\\\\implies 0.57 = e^{-0.0001t}\\\\\implies\ln \left(0.57\right)=-0.0001t\\\\t=-\frac{\ln \left(0.57\right)}{0.0001}[/tex]
Round to closest amount of years = 5621 years
Find the range of the parent function below. y = |x| A. all real numbers B. all positive numbers C. all positive numbers and 0 D. all negative numbers
Answer:
c
Step-by-step explanation:
absolute values are positive and abs value of 0 = 0
The following are the temperatures in
°C for the first 12 days of January:
-5.5, 6, -1.5, 3, 4, -2.5,
0, 6.5, -3, 2.5, -1, 5.5
What is the median temperature for
those 12 days?
Give your answer as a decimal.
ABC Check
↑
XI
Answer:
1.25 is the median for the first 12 days in January
-2+12-2^3 divided by 2^0 times 3
Answer:
The correct answer is -14
Step-by-step explanation:
If m∠B = 14°, and m∠D = 49°, what is m∠BEA?
Answer:
117 degrees
Step-by-step explanation:
A video game randomly chooses your car color and type. The
probability of getting a red car is 0.20, and the probability of
a getting a convertible is 0.30.
Event A = You get a red car.
Event B = You get a convertible.
A and B are independent events if
• A. The probability of getting a red car or a convertible is 0.06.
O
B. The probability of getting a red convertible is 0.06.
• C. The probability of getting a red car or a convertible is 0.50.
O D. The probability of getting a red convertible is 0.
The correct statement regarding when the events will be independent is given as follows:
B. The probability of getting a red convertible is 0.06.
What are independent events?Two events, A and B are independent, if:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem, the probabilities are given as follows:
P(A) = 0.2.P(B) = 0.3.The events will be independent if:
[tex]P(A \cap B) = 0.2 \times 0.3 = 0.06[/tex]
The intersection of events A and B is a red convertible car, hence the correct option is:
B. The probability of getting a red convertible is 0.06.
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Let [] denote the operation a [] b = a+b - [tex]\frac{ab}{2}[/tex] ....
The only statement that holds for the given operation is Statement II
Operations and numbersGiven the following operartions
a [] b = a+b - ab/2
We need to check the true statement
For the expression x [] (y+z) = x [] y + x [] z
x [] (y+z) = x+y+z - x(y+z)/2
x [] (y+z) = x+y+z - (xy+xz)/2
x [] y +x [] z = x+y - xy/2 +[x+z - xz/2 ]
x [] y +x [] z = x+y+x+z -xy/2 - xz/2
x [] y +x [] z = 2x+y+z - (xy+xz)/2
This shows that the statement I is incorrect
For the second statement
y [] z = y+z - yz/2
x [] (y [] z) = x + (y+z - yz/2) - x(y+z-yz/2)/2
x [] (y [] z) = x+y+z-yz/2 -xy/2 - xz/2+xyz/4
For the other expression
x [] y = x+y - xy/2
(x [] y) [] z = x+y - xy/2 + z - z(x+y - xy/2)/2
(x [] y) [] z = x+y+z- xy/2 -zx/2 - zy/2 + xyz/4
This shows that x [] (y [] z) = (x [] y) [] z is correct (Statement II)
For the third statement
x [] z = x+z - xz/2
y [] z = y+z - yz/2
z [] 0 = z+0 - z(0)/2
z [] 0 = z
x[]z + y[]z - z[]0 = x+z - xz/2 + y+z - yz/2 - z
x[]z + y[]z - z[]0 = x+y+z - xz/2 - yz/2
For the expression (x+y)[] z
(x+y)[] z = (x+y)+z - (xyz)/2
Hence the statement III is not valid
Based on the explanations above, the only statement that holds for the given operation is Statement II
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Which of the following is a true statement
5/6 > 10/12
8/16=1/4
3/4<4/6
11/15<4/5
Answer:
11/15 < 4/5
Step-by-step explanation:
1. 5/6 = 10/12, so the first answer is not correct
2. 1/4 = 4/16, so the second answer is not correct
3. 3/4 = 9/12 and 4/6 = 8/12, so the third answer is not correct
4. 4/5 = 12/15 > 11/15, so this answer is correct
Rewrite the expression with rational exponents as a radical expression by extending the properties of integer exponents.
two to the seven eighths power, all over two to the one fourth power
The expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.
What are Exponents?Exponents are the base raised to a power, It is written in the superscript of a number.
The expression given in the statement can be written as
[tex]\rm \dfrac{ 2^{7/8}}{2^{1/4}}[/tex]
By the Exponent rule,
[tex]\rm \dfrac{a^m}{a^n} = a^{m-n}[/tex]
So the expression can be written as
=[tex]\rm { 2^{7/8-1/4}[/tex]=[tex]\rm 2^{5/8}[/tex]
=[tex]\rm \sqrt[8]{2^5}[/tex]
Therefore, in radical form, the expression will be written as [tex]\rm \sqrt[8]{2^5}[/tex]., the correct option is A.
The complete question is
Rewrite the rational exponent as a radical by extending the properties of integer exponents.
2 to the 7 over 8 power, all over 2 to the 1 over 4 power
the eighth root of 2 to the fifth power
the fifth root of 2 to the eighth power
the square root of 2 to the 5 over 8 power
the fourth root of 2 to the sixth power
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A runner can run 3miles in 15 minutes. At this rate, how many miles can he run in 45minutes?
Answer:
9 miles
Step-by-step explanation:
If 3 miles is equal to 15 mins
Then you do 3 miles and times by 3 cause if you times 15 by 3, you'll get 45 mins
So the answer= 9 miles
Question 6 of 10
If and
A.D
BD B.C
are rational expressions, then:
OA. True
OB. False
The expression a/b ÷ c/d = ad/bc is A. true.
Given to show that if a/b and c/d are rational expressions, then a/b ÷ c/d = ad/bc.
The ratio of two polynomials is an example of a rational expression. If an expression f is rational, it can be expressed in the form p/q, where p and q are polynomials.
Here we have a ,b ,c and d in the form of p/q form.
We take the reciprocal of the expression on the right side of the division sign when the rational expression a/b is to be divided by the rational expression c/d.
so, L.H.S = a/b ÷ c/d
= a/b × 1/(c/d)
= a/b × d/c
= ad/bc
= R.H.S
since L.H.S = R.H.S
a/b ÷c/d = ad/bc
Hence the expression a/b ÷ c/d = ad/bc is A.true.
Your question was incomplete. Please find the missing content here.
If A/B and C/D are rational expressions, then: A/B ÷C/D
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PLEASE HELP ME! I WILL AWARD BRAINLIEST TO WHOEVER ANSWERS THE QUESTION BEST!
The Csc θ = [tex]\frac{8}{5}[/tex] is equivalent to which of the following expressions?
A. sin θ = [tex]\frac{5}{8}[/tex]
B. cos θ = [tex]\frac{5}{8}[/tex]
C. tan θ = [tex]\frac{5}{8}[/tex]
D. sin θ = [tex]\frac{8}{5}[/tex]
E. cos θ = [tex]\frac{8}{5}[/tex]
F. tan θ = [tex]\frac{8}{5}[/tex]
Answer:
A. sin θ = 5/8
Step-by-step explanation:
csc θ = 1/sin θ
csc θ = 8/5
1/sin θ = 8/5
sin θ = 5/8
Robert has 3/4 of a candy bar like he wants to share it with himself and two friends what fraction of the candy bar will each person get?
Answer:
significa que 1 barra de chocolate dividida entre 4 amigos es igual a 1 4. Por lo tanto, cada persona recibe 1 4 de la barra”. 6.
Step-by-step explanation:
Answer:
3/4 divided by 3 is 0.25
Step-by-step explanation:
We know that he has 3/4 of a candy bar and he wants to share it with himself plus 2 people.
The expression 3/4 divided by 3 represents this.
To change division to multiplication we use the reciprocal.
3/4 times 1/3 is 0.25.
Hope this helps. (:
Determine the equation of the linear function that generates the following table of values.
Answer:
y = -19x + 14
Step-by-step explanation:
For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14
Prove: m∠TSE + m∠RSO = m∠TSK
Answer:
down there
Step-by-step explanation:
we can see that angel rso and esk are congruent because they are verticle angels.
we also know that angel tse plus esk is equal to tsk, so angel tse+rso=tsk by algebra
sin A - sin B - sin C=-4cos A 2 .sin B 2 .sin C 2
sinA+sinB+sinC
=2sin(A+B)/2cos(A-B)/2+sin C
=2sin(pi-C)/2cos(A-B)/2+2sin C/2cosC/2
=2cosC/2(cos(A-B)/2+cos(A+B)/2)
=4 cos A/2 cos B/2 cos C/2
= RHS
The lines shown below are perpendicular.
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
The lines shown below are perpendicular. Is this statement true or false?
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
In order for a pair of lines to be perpendicular, they must intersect at a [tex]\bf{90^\circ}[/tex] angle. (a right angle)
[tex]\bf{Since\;the\;green\;line\;and\;the\;red\;one\;intersect\;at\;a\;right\;angle,}\\they\;are\;perpendicular.\\\\Hope\;you\;will\;have\;a\;fantabulous\;day!}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\boxed{\bf{aesthetic \not101}}[/tex]
Consider a banking system where the Federal Reserve uses required reserves to control the money supply. (This was the case in the U.S. prior to 2008.) Assume that banks do not hold excess reserves and that households do not hold currency, so the only form of money is demand deposits. To simplify the analysis, suppose the banking system has total reserves of $400. Determine the money multiplier and the money supply for each reserve requirement listed in the following table.
The determination of the money multiplier and the money supply for each reserve requirement listed in the following table are as follows:
Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5 20 $8,000
10 10 $4,000
What is the money multiplier?The money multiplier is the ratio of the reserve to the money supply.
The formula for determining the money multiplier is 1/r where r is the reserve ratio.
What is the money supply?The money supply is the total amount of money circulating in the commercial banking system.
The quantity of the money supply is determined by multiplying the money multiplier by the total reserves.
Data and Calculations:Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5 20 (1/0.05) $8,000 ($400 x 20)
10 10 (1/0.1) $4,000 ($400 x 10)
Question Completion:
Reserve Requirement Simple Money Money Supply
(percent) Multiplier (Dollars)
5
10
Thus, the money multiplier and money supply for the 5% reserve requirement are higher than for the 10% reserve requirement.
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Find the following sums ( for letter C)
Each number in the sum is even, so we can remove a factor of 2.
2 + 4 + 6 + 8 + ... + 78 + 80 = 2 (1 + 2 + 3 + 4 + ... + 39 + 40)
Use whatever technique you used in (a) and (b) to compute the sum
1 + 2 + 3 + 4 + ... + 39 + 40
With Gauss's method, for instance, we have
S = 1 + 2 + 3 + ... + 38 + 39 + 40
S = 40 + 39 + 38 + ... + 3 + 2 + 1
2S = (1 + 40) + (2 + 39) + ... + (39 + 2) + (40 + 1) = 40×41
S = 20×21 = 420
Then the sum you want is 2×420 = 840.
If there are 3 liquids in a Density column, which liquid would be the least dense?
The liquid on the bottom of the column.
The liquid floating on the top.
The liquid in between the liquid on the top of the column and the liquid on the bottom layer of the column.
The liquid that will be the least dense liquid in the density column is; The liquid floating on the top.
How to identify least dense liquid?
The formula for density is;
Density = Mass/Volume
Thus, the greater the mass, the more the density. Thus, it means that heavier objects will sink while lighter ones will float.
Thus, this means that the liquid that is most dense will be at the bottom of the liquid.
The liquid that is least dense will be at the top of the liquid.
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